Vibrational stability of double-star Roche model

• Published in: Astrophysics and space science Vol. 134; no. 1; pp. 55 - 71
• Main Author: KOPAL, Z
• Format: Journal Article
• Language: English
• Published: Dordrecht Kluwer 01.06.1987
• Subjects: Astronomy; Celestial mechanics (including n-body problems); Earth, ocean, space; Exact sciences and technology; Fundamental astronomy; Fundamental astronomy and astrophysics. Instrumentation, techniques, and astronomical observations; Dipole; Binary star; Restricted three body problem
• ISSN: 0004-640X; 1572-946X
• DOI: 10.1007/BF00636453

The Kopal (1980, 1987) methods are here extended by employing the Clairaut coordinates (in which the radial component is identified with the total potential) to analyze the nature of small oscillations about the equilibrium form of the Roche double-star model identical with zero-velocity surfaces of the restricted problem of three bodies. Linearized equations of this problem have been set up in Clairaut coordinates, and solved in a closed form. This solution turns out to be closely analogous to that obtained already for the rotating single-star Roche (1843) model, and discloses that (as in the preceding case) the terms that are secular in time already appear in the linear approximation. However, whether or not a retention of nonlinear terms in the equations of motion can regain secular stability of the respective configurations remains to be clarified by future investigations. (Author)